Not only is the topography challenging, it's high (9,380') and weather conditions rapidly become difficult as the sun warms the mountains and gets the convection going.
I haven't seem Lukla, but have seen Manang, which is west of Kathmandu and a little higher than Lukla. The one flight arrives early in the morning when it's still, flying up the valley below Annapurna which is one of the 8,000m peaks in Nepal. It lands up the strip, turns around, gets rid of the incoming pax and luggage, loads the outgoing asap, takes off down the strip and flies back down the valley towards Pokera. At the time at which this happens it's still. A bit later and the anabatic wind has started, and walking into it is an unpleasent experience.
So why do people take internal flights in Nepal? The roads in the mountains. Horrendous, as is the driving, and if you happen to look down the slopes you will often see wreckage below. One road we went along had two cracks on a corner, and the bit of road between them had dropped slightly and was probably waiting to get washed away in the next monsoon. I admit it is very difficult terrain to build roads in - lots of rather unstable glacial deposits - but the whole road travel experience in the mountains is hair-raising, and slow.